某些几何相交图类的局部认证
Local Certification of Some Geometric Intersection Graph Classes
AI总结：
本工作研究了分布式认证中几何相交图类的局部识别问题，为区间图、弦图、圆弧图、梯形图和置换图设计了具有对数大小证书的证明标记方案，并给出了紧致的对数下界。
摘要：
在分布式认证背景下，图类的识别已开始被密集研究。例如，最近获得了与平面图、有界树宽图和$H$-无小图识别相关的不同结果。本工作的目标是为相关几何相交图类（即区间图、弦图、圆弧图、梯形图和置换图）的局部识别设计紧凑的证书。更准确地说，我们给出了识别上述各类的证明标记方案，其使用对数大小的证书。我们还为上述任何几何相交图类的识别提供了证明标记方案中证书大小的紧致对数下界。
英文摘要：
In the context of distributed certification, the recognition of graph classes has started to be intensively studied. For instance, different results related to the recognition of planar, bounded tree-width and $H$-minor free graphs have been recently obtained. The goal of the present work is to design compact certificates for the local recognition of relevant geometric intersection graph classes, namely interval, chordal, circular arc, trapezoid and permutation. More precisely, we give proof labeling schemes recognizing each of these classes with logarithmic-sized certificates. We also provide tight logarithmic lower bounds on the size of the certificates on the proof labeling schemes for the recognition of any of the aforementioned geometric intersection graph classes.
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